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I wonder if some universities should pay more attention to the impact of discouragement on some students. I remember attempting a grad class called "Hard probl

I wonder if some universities should pay more attention to the impact of discouragement on some students. I remember attempting a grad class called "Hard problems in combinatorial optimization". I was struggling so I asked the professor for advice on getting my footing in the class. His answer was that I may just not have the "mathematical maturity" for the material. I was so discouraged that I dropped out of the program. What I didn't realize at the time was the particular meaning of that term. His advice was well intended and accurate. But what I heard was that I was hopeless in this topic area because I wasn't smart enough. So much pain could have been avoided if we just extended the conversation by a few minutes, or he invited me for a discussion over coffee.

treeman79 5y ago
First day of college algebra. Teacher shouted out “75% of you will drop out. Please leave now” 4 hours a night 6 days of week and I got a C. Less the 25% made it to end. Don’t think many of remaining passed. Got a lot out of it though.
- eigenket 5y ago
  That sounds like either an absolutely terrible teacher, or a terrible program. Why were so many people enrolled in a class that less than 25% would pass? I'm not American so I don't really understand the course names but I guess a class just called "Algebra" shouldn't be too hard? Stuff like basic groups/rings/fields or is it a more advanced class?
  - JadeNB 5y ago
    The title "College algebra" in the US indicates material that is well pre-groups/rings/etc.; it is about the basic skills of computations involving manipulation of variables, often involving such topics as solving linear and quadratic equations, and perhaps inequalities. At least at my university, the reason that such classes have a high failure rate is that the university is incentivized to have high enrollment numbers by admitting students who do not have the background to succeed at college mathematics at the level of calculus or above, and so need some pre-calculus courses; but someone who does not have a solid grounding in pre-calculus mathematics will often struggle to learn it when it is taught at a rapid pace at the college level—especially by professors most of whose teaching experience is with college-level math.
    - eigenket 5y ago
      But what incentivises the students to take a class that so many won't pass? I don't really understand the American university system but surely the sensible choice would be to take a course you're most likely to pass? I guess its possible to learn stuff from a course you fail, but you should be able to find a course that you're likely to pass and learn something from?
      - Jtsummers 5y ago
        It's mandatory for the degree, that's the motivation. It's typically required for all students who didn't score high enough on entrance exams or take enough math courses in high school. They also likely don't talk to their advisor and say, "I want to take something else, like prob/stat or calculus, to substitute for this requirement." STEM majors will find it easier to substitute another course than non-STEM majors (because they likely have the background to skip it from HS course work). Engineering universities and the like usually send their first year students straight to calculus, though.
        eigenket 5y ago
        So the 75%+ who don't pass this course don't graduate or what? They have to change degree?
        Jtsummers 5y ago
        I've never heard of so many failing a college algebra course, at my second university it was around 25% failing and mostly because they'd relaxed the entry requirements in order to increase enrollment. However, for non-STEM and non-Business majors college algebra is rarely a prerequisite for any other courses so you can still continue your major without it, you do need to pass a math course before graduating though. They also have other math courses that can be used that aren't college algebra and may be easier.
        nick__m 5y ago
        At my university, CS was called math-CS, it required intenses calculus courses with a similar failure rate. Of those who failed : ¼ retook the course, ¼ pivoted to the bussines-CS program (given by the CS department) , ¼ pivoted to bussines-IT (given by the business and management school) and as far as I know, the rest disappeared from the university.
  - marktangotango 5y ago
    > Stuff like basic groups/rings/fields or is it a more advanced class? No, it's usually basics like functions, graphs, and trigonometry. It's basically a remedial class for what students didn't learn in highschool.
    - eigenket 5y ago
      Maybe I'm massively out of touch but I'm pretty sure a good teacher could teach that stuff to almost anyone. Like this stuff isn't particularly complicated, I'm not a very good teacher but I did teach some undergrad seminars during my PhD and I think even my worst students were capable of understanding functions, graphs and trig.
      - zozbot234 5y ago
        That's not the issue. College algebra courses are super compressed, they're basically trying to teach the whole of junior high + high school math in a single semester. That's barely teaching, and the natural outcome of such a cursorily taught course is to act as a 'weedout' course.
        brimble 5y ago
        Yup. My observation (having not had to take College Algebra myself, but knowing people who did) is that it's a class to make sure people who fell off the math train back at operations on fractions or factoring or whatever, don't get any farther.
        JohnWhigham 5y ago
        I mean, what do you want them to do? Invest resources in splitting up material into multiple courses when they should have learned it before even coming to college? It's not their fault public schools suck.
        ghaff 5y ago
        All public schools do not suck but especially urban schools can have a lot of problems and many of the students don't have a great home environment either,
- spaniard89277 5y ago
  Hah that sounds exactly like my uni.
strikelaserclaw 5y ago
You think Mathematicians in general have people skills? Most Mathematicians i met were good people but they definitely kinda lived in their own world, they were super helpful, but only if you explicitly asked for their help.
- zozbot234 5y ago
  People skills? The informal prereqs/expected background for a class should be listed in the syllabus. Lack of "mathematical maturity" is a non-answer, they should make it clear what sort of math knowledge that refers to.
  - strikelaserclaw 5y ago
    Maybe the class did have pre-req? I mean i think it is obvious that a class called "Hard problems in combinatorial optimization" is aimed more at future Mathematicians/Computer Scientists than people who want to take it for the fun of it.
  - patrickthebold 5y ago
    I disagree. 'Mathematical maturity', to me, means: There is no specific advanced prerequisite knowledge, but you need to be able to follow something technical. As an example: you'd reasonably expect a student with mathematical maturity to know what a set, the Cartesian product of two sets, and a function are. That's high school level math. From there you can define a ring and a module over a ring, in like 5 mins. So at that point the Prof, strictly speaking, told you everything you need to know to start studying modules. Of course, many students will be like whaaaaaa?! When a ring is defined. But here's the point: Mathematical maturity does not mean that you already know what a ring is, but when the Prof defines a ring, you are following along. Anyway, my point is that there is nothing specific that you need to know.
    - woah 5y ago
      Isnt' that basic set theory as a prereq
cehrlich 5y ago
I obviously don't know your specific situation, but often this is the result of idiotic cost cutting measures by universities. As a lecturer, I've had several job interviews where half of the questions were some variety of "are you ok to put up with having way too many students and not enough time?". I had the luxury of not having to take these jobs, but obviously someone ended up taking them.
chrisco255 5y ago
Maybe they should teach self esteem and resiliency in the face of criticism and failure, because you will definitely be criticized and you'll definitely fail. You will face setbacks and discouragement at many points in your life. More often than not, your biggest critic will be yourself. That much is certain. This wasn't even really intentional discouragement, but it was perceived as such. Hopefully, you learned the higher lesson.
- PuppyTailWags 5y ago
  You can have plenty of self esteem and resiliency and also decide based on evidence that an activity may not be the best use of your time. If you respect a teacher's evaluation of your performance in a subject and the teacher's evaluation is that you don't have the maturity to learn from them, it may make much more sense to try other things than insist on forcing them to teach you anyways. People don't have to intend to say cruel things in order to be cruel-- for example, you don't have to intend to hurt someone who recently miscarried by talking about your successful pregnancy and its definitely not considered the fault of the person who is grieving. Similarly a professor doesn't have to intend to be discouraging in order to be discouraging.
- fleetwoodsnack 5y ago
  I think we can reasonably argue that the statement is overdetermined. Charitably, perhaps the professor did mean mathematical maturity in the sense of "try learning some background first, and give yourself the time to let your skills and intuition develop." Uncharitably, perhaps the professor did not, and meant mathematical maturity in the sense of, "you have an inherent deficiency that makes this an inappropriate undertaking for you." I think where the fruit of this discussion may be is deciding to what degree an authority figure like a professor has a responsibility or an obligation to their students and advisees to make themselves clear which way they intend their statements to be interpreted. Personally, this begets a discussion of the nuances between the obligations and responsibilities of communication between (1) strangers, (2) peers/colleagues, and (3) authority figures and their charges.
jdkjs 5y ago
How did you interpret “immature” as “not smart enough”? A baby is not mature, which doesn’t mean he won’t grow up. “Immaturity” means that there’s room for improvement and that that improvement is attainable. What I mean to say is that this issue stems from your misunderstanding of the meaning of the word “mature” and nothing else.
- CoastalCoder 5y ago
  It's been a long time, but IIRC I recognized that my understanding of the term was vague but that all interpretations boiled down to, if I wasn't ready now I never would be. I'm not claiming that my response was entirely rational or measured. I'm not blaming the professor, and I'm not justifying my own reaction. I was just saying what my reaction was, in case it shows a pattern of student experiences that's worth addressing.
  - robocat 5y ago
    If you have reasonable people skills, you may well have correctly inferred what the lecturer was communicating: overly questioning the words can be damaging. As I have matured, I have learnt better to trust my intuitive reading of what someone says, especially when I detect that the meaning of their words is divergent from what I believe they think beneath the surface. Stubbornness, tenacity and self-belief are useful skills for success - perhaps you gave up too quickly? Unfortunately, soft skills are very rarely taught well. We all rely upon our subconscious learning and a good amount of luck to gain necessary skills, and those skills are often learnt by osmosis while very young. I also think the meta-skill of being able to teach yourself soft skills is not common either and it - although we can make an effort to improve that meta-skill even though it is somewhat self-referential.
- whoisburbansky 5y ago
  Assuming OP was an undergrad, it’s totally fair to assume that the prof in question was trying to euphemistically say that they weren’t good enough for the class, especially since “mathematical maturity” is something of a term of art in the field. I don’t think it’s worth putting down teenagers for not understanding the nuances of every single bit of terminology in a field they’re dipping their toes into, the expectation should be that professors be more empathetic to that.
emeraldd 5y ago
> His answer was that I may just not have the "mathematical maturity" for the material. I was so discouraged that I dropped out of the program. There's a problem with making a statement like that and not following it up with what you need to do gain the needed "maturity". Even adding "maybe you should take this course over here and come back to this one in a semester..." could make a world of difference.
- agumonkey 5y ago
  I think usually it boils down to teachers in advanced schools were the kind of pupils who got most things easily and have no clue how to explain things more than <list of set comprehension>. Got me to think that these universities are more magnets from strong ex-pupils to similar minded new pupils that will fit in without much pedagogical efforts.
  - User23 5y ago
    The average IQ of math majors is absurdly high, more than two sigma above the mean[1]. In an organization like that the smartest person is likely going to be a breathtaking five sigma above the general population mean[2]. I get the impression that people in math departments like it that way, so weeding out persons of more ordinary intelligence is more of a feature than a bug. I doubt many would admit to that, but it fits the observables. [1] https://chhaylinlim.wordpress.com/2014/09/24/average-iq-per-college-major/ https://chhaylinlim.wordpress.com/2014/09/24/average-iq-per-... [2] Assuming gaussian distribution with no skew, which is probably a bad assumption, but I'm spitballing here. Suffice to say math departments at elite colleges have many extremely bright people.
    - cjbgkagh 5y ago
      IQ has no skew by definition. That said, I think there are a number of IQ boosting mutations and innate mathematical aptitude is likely correlated to possession of one or more of these rare(ish) mutations.
      - 5y ago
dkarl 5y ago
I think this happens a lot. For some reason people have a really strong tendency with math to attribute it to innate talent. Of course talent matters, but people get hung up on it and discount other factors. The word "maturity" is supposed to help indicate that it's a matter of having and digesting the right experiences, but it honestly isn't great, because maturity can be driven by experience, but it can also be dictated by biology. If someone is isolated from human contact between the ages of ten and twenty, they will emerge fully mature in some ways and immature in others. We need a less ambiguous way of saying that somebody hasn't yet had the exposure and practice that will prepare them to tackle certain material.
avg_dev 5y ago
Can you explain the particular meaning of that term for the rest of us?
- tzs 5y ago
  The Wikipedia article on it is pretty good: https://en.wikipedia.org/wiki/Mathematical_maturity https://en.wikipedia.org/wiki/Mathematical_maturity
buescher 5y ago
The old joke about sufficient "mathematical maturity" is "write a lowercase zeta".
agumonkey 5y ago
I thought about this a lot. In college I often failed and teacher would look at me dumbfounded (followed by the traditional "it's trivial"). Very discouraging indeed. Years later I revisit some things, and without struggling too much, I get insights and ideas and overall easier time actually solving things. So in the end it does look like some "maturity" was lacking. Now it's bothersome that schools can only operate on people with magic maturity and other people are left on the side (the school as semi-comb theory) and I wish we could have some pedagogical light on what is that missing maturity and how to grow it explicitely.
jimbokun 5y ago
> So much pain could have been avoided if we just extended the conversation by a few minutes, or he invited me for a discussion over coffee. Or if you had the maturity to accept criticism like an adult.
- julianeon 5y ago
  I’m not sure that college students - or, to call them by their age group, teenagers - are really appropriately assumed to be “adults” at all times. Obviously we don’t think that when it comes to alcohol and partying - universities step in and make heavy-handed decisions we’d never apply to full adults all the time (example, shutting down a house & evicting residents for having a party where an assault happened). So why not apply that same “not yet fully mature adults” logic when it comes to something with massive social benefits, which society has in interest in promoting: more mathematically literate university graduates?
- zhengyi13 5y ago
  This is precisely what first year students are not.
crispyambulance 5y ago
> [...] may just not have the "mathematical maturity" for the material. LOTS of non-math-major science/engineering students face that problem as soon as they start grad school. It's a consequence, IMHO, of math curriculums failing to focus on the fundamentals rigorously enough. There's too much focus on what we used to call "plug-n-chug" mathematics where students learn just enough to apply formulae to get their problems solved. It might seem like "just enough" but it ends up pushing out higher mathematics and keeps students from being able to apply more advanced mathematical concepts that they would have gained from a much deeper dive into Real Analysis, abstract algebra, differential geometry, etc, and the grind of the theorem-proof cycles. Many of us felt this right away upon taking graduate level courses. I wish that I had been counseled to take additional math courses before (or even at the beginning) of grad school. It would have reduced my suffering A LOT and I would have gotten more out of the degree.
- JackFr 5y ago
  I thought I had it - lots of real analysis and abstract algebra proofs - but then in grad school I hit a 400 level numerical methods class that I simply lacked the mathematical sophistication for. Just completely at sea - an experience which I lacked the academic maturity to deal with.
JackFr 5y ago
> What I didn't realize at the time was the particular meaning of that term. His advice was well intended and accurate. I had a similar experience - and while it was a blow to my confidence I’m happy that he didn’t tiptoe around it with feel-goodisms. What I was doing as a student, and what had ben successful so far, was not working and doing more of it or doing it harder wasn’t going to help. Honestly leaving that program was the right thing to do, I probably shouldn’t have been in it, though I’m confident a few years later I would have been successful, but I lacked the maturity and mathematical sophistication to get it then.
snapetom 5y ago
I wonder if the whole "weeding out" theory extends to college education in general, and like you ask, how constructive to society that is. I, very briefly and quite honestly, attended a lower tier state school that was an absolute joke. Shortly after I started, there was an outreach program for local high school kids where if they showed a high school ID, they got admission for the upcoming year. The head of my dept dismissed it and quipped, "It's ok. Anyone that wasn't meant to be here will just drop out after a year anyway and we have their money." I, thankfully, ended up at a much bigger P5, well-known university. One of the controversies was the engineering departments were trying to get as many students as possible to the point of exceeding infrastructure and admitting lower quality students into the program. Upperclassmen I talk to said, "that's why everyone hates <1st semester math for engineers> and <2nd semester math for engineers>. They immediately weed out those that don't qualify." "Weeding out" is what college admissions should be doing, not the departments. When the departments weed someone out, they've wasted at least a year of their life and a year in tuition, and demoralized them. This is what really the "college for everyone" mentality has led to. If the kid shouldn't be there, or should have started in junior college first, we need to be more upfront about that earlier.
- whatshisface 5y ago
  >"Weeding out" is what college admissions should be doing, not the departments. When the departments weed someone out, they've wasted at least a year of their life and a year in tuition, and demoralized them. Admissions can't weed people out, they can only copy the weeding that highschool has done. If you rephrases the question that way, as in, "should highschool teachers be responsible for college admissions," then the idea of letting people join a major they haven't proven themselves capable of doesn't sound so bad after all.
- bjourne 5y ago
  I disagree with that. Even if someone fails all their classes in their first year the experience will teach them much more about life than any job would. The real problem is that US universities cost a lot of money so the cost of failure is insane.
ChicagoBoy11 5y ago
This is a really deep point. A math professor at The University of Chicago wisely pointed to me as this being a super important thing to keep in mind when teaching (I've gone into secondary education). Often the material you are and how well the student is receiving has a much smaller impact on the student than what the emotional experience of it communicates to them about their own capabilities, including their chance at continue to struggle through the material in the hopes of fully grasping it. Especially in the latter years in school, it seems you find a lot of teachers who almost revel in making their courses "impossible" for kids, which can sometimes be very motivational for extremely high-achievers but absolutely devastating to a well-intentioned student who is having a challenge with the material.
- msteffen 5y ago
  Another UChicago student here (former math major). I think the UChicago math department took education seriously in a unique way that I wish they got more credit for; the Inquiry-Based Learning classes, the summer classes for Chicago public school teachers, and the Research Experience for Undergraduates were all pretty special, I think. Also, the math classes all had a shared policy of "you can work with anyone you like on a problem set, as long as everyone's name is listed on there when you hand it in." I loved that, and I did all my problem sets in groups while I was there, and I think I learned more because we were always explaining things to each other and arguing about solutions. I heard a rumor at one point that this policy was the direct product of Peter May's bad experience at Princeton, which required students to work alone when he was there. TFA does seem like a pretty stinging indictment of Princeton's math department.
pmontra 5y ago
Maybe they are interested only in future Ph.Ds and Professors. Anybody else is a burden to be sent somewhere else as soon as possible. Maybe they think they're doing a favor to those students because they won't be wasting their time on subjects that are too difficult for them to grasp in the short time of a university class.
cannabis_sam 5y ago
> His answer was that I may just not have the "mathematical maturity" for the material. What a clueless, absolute piece of shit.. Clearly he lacks the emotional maturity to deal with students (or just people in general) and unequivocally should be fired as a teacher and restricted to doing research.

treeman79 5y ago

First day of college algebra. Teacher shouted out “75% of you will drop out. Please leave now” 4 hours a night 6 days of week and I got a C. Less the 25% made it to end. Don’t think many of remaining passed. Got a lot out of it though.

eigenket 5y ago
That sounds like either an absolutely terrible teacher, or a terrible program. Why were so many people enrolled in a class that less than 25% would pass? I'm not American so I don't really understand the course names but I guess a class just called "Algebra" shouldn't be too hard? Stuff like basic groups/rings/fields or is it a more advanced class?
- JadeNB 5y ago
  The title "College algebra" in the US indicates material that is well pre-groups/rings/etc.; it is about the basic skills of computations involving manipulation of variables, often involving such topics as solving linear and quadratic equations, and perhaps inequalities. At least at my university, the reason that such classes have a high failure rate is that the university is incentivized to have high enrollment numbers by admitting students who do not have the background to succeed at college mathematics at the level of calculus or above, and so need some pre-calculus courses; but someone who does not have a solid grounding in pre-calculus mathematics will often struggle to learn it when it is taught at a rapid pace at the college level—especially by professors most of whose teaching experience is with college-level math.
  - eigenket 5y ago
    But what incentivises the students to take a class that so many won't pass? I don't really understand the American university system but surely the sensible choice would be to take a course you're most likely to pass? I guess its possible to learn stuff from a course you fail, but you should be able to find a course that you're likely to pass and learn something from?
    - Jtsummers 5y ago
      It's mandatory for the degree, that's the motivation. It's typically required for all students who didn't score high enough on entrance exams or take enough math courses in high school. They also likely don't talk to their advisor and say, "I want to take something else, like prob/stat or calculus, to substitute for this requirement." STEM majors will find it easier to substitute another course than non-STEM majors (because they likely have the background to skip it from HS course work). Engineering universities and the like usually send their first year students straight to calculus, though.
      - eigenket 5y ago
        So the 75%+ who don't pass this course don't graduate or what? They have to change degree?
        Jtsummers 5y ago
        I've never heard of so many failing a college algebra course, at my second university it was around 25% failing and mostly because they'd relaxed the entry requirements in order to increase enrollment. However, for non-STEM and non-Business majors college algebra is rarely a prerequisite for any other courses so you can still continue your major without it, you do need to pass a math course before graduating though. They also have other math courses that can be used that aren't college algebra and may be easier.
        nick__m 5y ago
        At my university, CS was called math-CS, it required intenses calculus courses with a similar failure rate. Of those who failed : ¼ retook the course, ¼ pivoted to the bussines-CS program (given by the CS department) , ¼ pivoted to bussines-IT (given by the business and management school) and as far as I know, the rest disappeared from the university.
- marktangotango 5y ago
  > Stuff like basic groups/rings/fields or is it a more advanced class? No, it's usually basics like functions, graphs, and trigonometry. It's basically a remedial class for what students didn't learn in highschool.
  - eigenket 5y ago
    Maybe I'm massively out of touch but I'm pretty sure a good teacher could teach that stuff to almost anyone. Like this stuff isn't particularly complicated, I'm not a very good teacher but I did teach some undergrad seminars during my PhD and I think even my worst students were capable of understanding functions, graphs and trig.
    - zozbot234 5y ago
      That's not the issue. College algebra courses are super compressed, they're basically trying to teach the whole of junior high + high school math in a single semester. That's barely teaching, and the natural outcome of such a cursorily taught course is to act as a 'weedout' course.
      - brimble 5y ago
        Yup. My observation (having not had to take College Algebra myself, but knowing people who did) is that it's a class to make sure people who fell off the math train back at operations on fractions or factoring or whatever, don't get any farther.
      - JohnWhigham 5y ago
        I mean, what do you want them to do? Invest resources in splitting up material into multiple courses when they should have learned it before even coming to college? It's not their fault public schools suck.
        ghaff 5y ago
        All public schools do not suck but especially urban schools can have a lot of problems and many of the students don't have a great home environment either,
spaniard89277 5y ago
Hah that sounds exactly like my uni.

strikelaserclaw 5y ago

You think Mathematicians in general have people skills? Most Mathematicians i met were good people but they definitely kinda lived in their own world, they were super helpful, but only if you explicitly asked for their help.

zozbot234 5y ago
People skills? The informal prereqs/expected background for a class should be listed in the syllabus. Lack of "mathematical maturity" is a non-answer, they should make it clear what sort of math knowledge that refers to.
- strikelaserclaw 5y ago
  Maybe the class did have pre-req? I mean i think it is obvious that a class called "Hard problems in combinatorial optimization" is aimed more at future Mathematicians/Computer Scientists than people who want to take it for the fun of it.
- patrickthebold 5y ago
  I disagree. 'Mathematical maturity', to me, means: There is no specific advanced prerequisite knowledge, but you need to be able to follow something technical. As an example: you'd reasonably expect a student with mathematical maturity to know what a set, the Cartesian product of two sets, and a function are. That's high school level math. From there you can define a ring and a module over a ring, in like 5 mins. So at that point the Prof, strictly speaking, told you everything you need to know to start studying modules. Of course, many students will be like whaaaaaa?! When a ring is defined. But here's the point: Mathematical maturity does not mean that you already know what a ring is, but when the Prof defines a ring, you are following along. Anyway, my point is that there is nothing specific that you need to know.
  - woah 5y ago
    Isnt' that basic set theory as a prereq

cehrlich 5y ago

I obviously don't know your specific situation, but often this is the result of idiotic cost cutting measures by universities. As a lecturer, I've had several job interviews where half of the questions were some variety of "are you ok to put up with having way too many students and not enough time?". I had the luxury of not having to take these jobs, but obviously someone ended up taking them.

chrisco255 5y ago

Maybe they should teach self esteem and resiliency in the face of criticism and failure, because you will definitely be criticized and you'll definitely fail. You will face setbacks and discouragement at many points in your life. More often than not, your biggest critic will be yourself. That much is certain. This wasn't even really intentional discouragement, but it was perceived as such. Hopefully, you learned the higher lesson.

PuppyTailWags 5y ago
You can have plenty of self esteem and resiliency and also decide based on evidence that an activity may not be the best use of your time. If you respect a teacher's evaluation of your performance in a subject and the teacher's evaluation is that you don't have the maturity to learn from them, it may make much more sense to try other things than insist on forcing them to teach you anyways. People don't have to intend to say cruel things in order to be cruel-- for example, you don't have to intend to hurt someone who recently miscarried by talking about your successful pregnancy and its definitely not considered the fault of the person who is grieving. Similarly a professor doesn't have to intend to be discouraging in order to be discouraging.
fleetwoodsnack 5y ago
I think we can reasonably argue that the statement is overdetermined. Charitably, perhaps the professor did mean mathematical maturity in the sense of "try learning some background first, and give yourself the time to let your skills and intuition develop." Uncharitably, perhaps the professor did not, and meant mathematical maturity in the sense of, "you have an inherent deficiency that makes this an inappropriate undertaking for you." I think where the fruit of this discussion may be is deciding to what degree an authority figure like a professor has a responsibility or an obligation to their students and advisees to make themselves clear which way they intend their statements to be interpreted. Personally, this begets a discussion of the nuances between the obligations and responsibilities of communication between (1) strangers, (2) peers/colleagues, and (3) authority figures and their charges.

jdkjs 5y ago

How did you interpret “immature” as “not smart enough”? A baby is not mature, which doesn’t mean he won’t grow up. “Immaturity” means that there’s room for improvement and that that improvement is attainable. What I mean to say is that this issue stems from your misunderstanding of the meaning of the word “mature” and nothing else.

CoastalCoder 5y ago
It's been a long time, but IIRC I recognized that my understanding of the term was vague but that all interpretations boiled down to, if I wasn't ready now I never would be. I'm not claiming that my response was entirely rational or measured. I'm not blaming the professor, and I'm not justifying my own reaction. I was just saying what my reaction was, in case it shows a pattern of student experiences that's worth addressing.
- robocat 5y ago
  If you have reasonable people skills, you may well have correctly inferred what the lecturer was communicating: overly questioning the words can be damaging. As I have matured, I have learnt better to trust my intuitive reading of what someone says, especially when I detect that the meaning of their words is divergent from what I believe they think beneath the surface. Stubbornness, tenacity and self-belief are useful skills for success - perhaps you gave up too quickly? Unfortunately, soft skills are very rarely taught well. We all rely upon our subconscious learning and a good amount of luck to gain necessary skills, and those skills are often learnt by osmosis while very young. I also think the meta-skill of being able to teach yourself soft skills is not common either and it - although we can make an effort to improve that meta-skill even though it is somewhat self-referential.
whoisburbansky 5y ago
Assuming OP was an undergrad, it’s totally fair to assume that the prof in question was trying to euphemistically say that they weren’t good enough for the class, especially since “mathematical maturity” is something of a term of art in the field. I don’t think it’s worth putting down teenagers for not understanding the nuances of every single bit of terminology in a field they’re dipping their toes into, the expectation should be that professors be more empathetic to that.

emeraldd 5y ago

> His answer was that I may just not have the "mathematical maturity" for the material. I was so discouraged that I dropped out of the program. There's a problem with making a statement like that and not following it up with what you need to do gain the needed "maturity". Even adding "maybe you should take this course over here and come back to this one in a semester..." could make a world of difference.

agumonkey 5y ago
I think usually it boils down to teachers in advanced schools were the kind of pupils who got most things easily and have no clue how to explain things more than <list of set comprehension>. Got me to think that these universities are more magnets from strong ex-pupils to similar minded new pupils that will fit in without much pedagogical efforts.
- User23 5y ago
  The average IQ of math majors is absurdly high, more than two sigma above the mean[1]. In an organization like that the smartest person is likely going to be a breathtaking five sigma above the general population mean[2]. I get the impression that people in math departments like it that way, so weeding out persons of more ordinary intelligence is more of a feature than a bug. I doubt many would admit to that, but it fits the observables. [1] https://chhaylinlim.wordpress.com/2014/09/24/average-iq-per-college-major/ https://chhaylinlim.wordpress.com/2014/09/24/average-iq-per-... [2] Assuming gaussian distribution with no skew, which is probably a bad assumption, but I'm spitballing here. Suffice to say math departments at elite colleges have many extremely bright people.
  - cjbgkagh 5y ago
    IQ has no skew by definition. That said, I think there are a number of IQ boosting mutations and innate mathematical aptitude is likely correlated to possession of one or more of these rare(ish) mutations.
    - 5y ago

dkarl 5y ago

I think this happens a lot. For some reason people have a really strong tendency with math to attribute it to innate talent. Of course talent matters, but people get hung up on it and discount other factors. The word "maturity" is supposed to help indicate that it's a matter of having and digesting the right experiences, but it honestly isn't great, because maturity can be driven by experience, but it can also be dictated by biology. If someone is isolated from human contact between the ages of ten and twenty, they will emerge fully mature in some ways and immature in others. We need a less ambiguous way of saying that somebody hasn't yet had the exposure and practice that will prepare them to tackle certain material.

avg_dev 5y ago

Can you explain the particular meaning of that term for the rest of us?

tzs 5y ago
The Wikipedia article on it is pretty good: https://en.wikipedia.org/wiki/Mathematical_maturity https://en.wikipedia.org/wiki/Mathematical_maturity

buescher 5y ago

The old joke about sufficient "mathematical maturity" is "write a lowercase zeta".

agumonkey 5y ago

I thought about this a lot. In college I often failed and teacher would look at me dumbfounded (followed by the traditional "it's trivial"). Very discouraging indeed. Years later I revisit some things, and without struggling too much, I get insights and ideas and overall easier time actually solving things. So in the end it does look like some "maturity" was lacking. Now it's bothersome that schools can only operate on people with magic maturity and other people are left on the side (the school as semi-comb theory) and I wish we could have some pedagogical light on what is that missing maturity and how to grow it explicitely.

jimbokun 5y ago

> So much pain could have been avoided if we just extended the conversation by a few minutes, or he invited me for a discussion over coffee. Or if you had the maturity to accept criticism like an adult.

julianeon 5y ago
I’m not sure that college students - or, to call them by their age group, teenagers - are really appropriately assumed to be “adults” at all times. Obviously we don’t think that when it comes to alcohol and partying - universities step in and make heavy-handed decisions we’d never apply to full adults all the time (example, shutting down a house & evicting residents for having a party where an assault happened). So why not apply that same “not yet fully mature adults” logic when it comes to something with massive social benefits, which society has in interest in promoting: more mathematically literate university graduates?
zhengyi13 5y ago
This is precisely what first year students are not.

crispyambulance 5y ago

> [...] may just not have the "mathematical maturity" for the material. LOTS of non-math-major science/engineering students face that problem as soon as they start grad school. It's a consequence, IMHO, of math curriculums failing to focus on the fundamentals rigorously enough. There's too much focus on what we used to call "plug-n-chug" mathematics where students learn just enough to apply formulae to get their problems solved. It might seem like "just enough" but it ends up pushing out higher mathematics and keeps students from being able to apply more advanced mathematical concepts that they would have gained from a much deeper dive into Real Analysis, abstract algebra, differential geometry, etc, and the grind of the theorem-proof cycles. Many of us felt this right away upon taking graduate level courses. I wish that I had been counseled to take additional math courses before (or even at the beginning) of grad school. It would have reduced my suffering A LOT and I would have gotten more out of the degree.

JackFr 5y ago
I thought I had it - lots of real analysis and abstract algebra proofs - but then in grad school I hit a 400 level numerical methods class that I simply lacked the mathematical sophistication for. Just completely at sea - an experience which I lacked the academic maturity to deal with.

JackFr 5y ago

> What I didn't realize at the time was the particular meaning of that term. His advice was well intended and accurate. I had a similar experience - and while it was a blow to my confidence I’m happy that he didn’t tiptoe around it with feel-goodisms. What I was doing as a student, and what had ben successful so far, was not working and doing more of it or doing it harder wasn’t going to help. Honestly leaving that program was the right thing to do, I probably shouldn’t have been in it, though I’m confident a few years later I would have been successful, but I lacked the maturity and mathematical sophistication to get it then.

snapetom 5y ago

I wonder if the whole "weeding out" theory extends to college education in general, and like you ask, how constructive to society that is. I, very briefly and quite honestly, attended a lower tier state school that was an absolute joke. Shortly after I started, there was an outreach program for local high school kids where if they showed a high school ID, they got admission for the upcoming year. The head of my dept dismissed it and quipped, "It's ok. Anyone that wasn't meant to be here will just drop out after a year anyway and we have their money." I, thankfully, ended up at a much bigger P5, well-known university. One of the controversies was the engineering departments were trying to get as many students as possible to the point of exceeding infrastructure and admitting lower quality students into the program. Upperclassmen I talk to said, "that's why everyone hates <1st semester math for engineers> and <2nd semester math for engineers>. They immediately weed out those that don't qualify." "Weeding out" is what college admissions should be doing, not the departments. When the departments weed someone out, they've wasted at least a year of their life and a year in tuition, and demoralized them. This is what really the "college for everyone" mentality has led to. If the kid shouldn't be there, or should have started in junior college first, we need to be more upfront about that earlier.

whatshisface 5y ago
>"Weeding out" is what college admissions should be doing, not the departments. When the departments weed someone out, they've wasted at least a year of their life and a year in tuition, and demoralized them. Admissions can't weed people out, they can only copy the weeding that highschool has done. If you rephrases the question that way, as in, "should highschool teachers be responsible for college admissions," then the idea of letting people join a major they haven't proven themselves capable of doesn't sound so bad after all.
bjourne 5y ago
I disagree with that. Even if someone fails all their classes in their first year the experience will teach them much more about life than any job would. The real problem is that US universities cost a lot of money so the cost of failure is insane.

ChicagoBoy11 5y ago

This is a really deep point. A math professor at The University of Chicago wisely pointed to me as this being a super important thing to keep in mind when teaching (I've gone into secondary education). Often the material you are and how well the student is receiving has a much smaller impact on the student than what the emotional experience of it communicates to them about their own capabilities, including their chance at continue to struggle through the material in the hopes of fully grasping it. Especially in the latter years in school, it seems you find a lot of teachers who almost revel in making their courses "impossible" for kids, which can sometimes be very motivational for extremely high-achievers but absolutely devastating to a well-intentioned student who is having a challenge with the material.

msteffen 5y ago
Another UChicago student here (former math major). I think the UChicago math department took education seriously in a unique way that I wish they got more credit for; the Inquiry-Based Learning classes, the summer classes for Chicago public school teachers, and the Research Experience for Undergraduates were all pretty special, I think. Also, the math classes all had a shared policy of "you can work with anyone you like on a problem set, as long as everyone's name is listed on there when you hand it in." I loved that, and I did all my problem sets in groups while I was there, and I think I learned more because we were always explaining things to each other and arguing about solutions. I heard a rumor at one point that this policy was the direct product of Peter May's bad experience at Princeton, which required students to work alone when he was there. TFA does seem like a pretty stinging indictment of Princeton's math department.

pmontra 5y ago

Maybe they are interested only in future Ph.Ds and Professors. Anybody else is a burden to be sent somewhere else as soon as possible. Maybe they think they're doing a favor to those students because they won't be wasting their time on subjects that are too difficult for them to grasp in the short time of a university class.

cannabis_sam 5y ago

> His answer was that I may just not have the "mathematical maturity" for the material. What a clueless, absolute piece of shit.. Clearly he lacks the emotional maturity to deal with students (or just people in general) and unequivocally should be fired as a teacher and restricted to doing research.